A new approach to problem solving is proposed for multiple-solution problems in a mental search task. Subjects will first memorize a list of words, and then search mentally through the list for answers to questions. The answers will be recorded along with the inter-response times between answers. This will allow a comparison between two posible search strategies: sampling with replacement and sampling without replacement. The former strategy has been a part of most traditional models of problem solving, while the latter represents a new approach. Preliminary results have been largely in agreement with the sampling-without-replacement strategy. Further analyses of the results have led to a more detailed additive time component model. This model is based on the independent summation of (a) read-in time, (b) memory-retrieval time, (c) decision-making time, and (d) response- output time. The goals of the proposed research are (1) to evaluate the use of multiple-solution problems in the study of problem solving, (2) to explore the psychological processes involved in problem solving, (3) to test a new model of problem solving behavior, and (4) to compare this model with more traditional models of problem solving.